Davide Castelvecchi at Nature has the story this morning of a press conference held earlier today at Kyoto University to announce the publication by Publications of the Research Institute for Mathematical Sciences (RIMS) of Mochizuki’s purported proof of the abc conjecture.
This is very odd. As the Nature subheadline explains, “some experts say author Shinichi Mochizuki failed to fix fatal flaw”. It’s completely unheard of for a major journal to publish a proof of an important result when experts have publicly stated that the proof is flawed and are standing behind that statement. That Mochizuki is the chief editor of the journal and that the announcement was made by two of his RIMS colleagues doesn’t help at all with the situation.
For background on the problem with the proof, see an earlier blog entry here. In the Nature article Peter Scholze states:
My judgment has not changed in any way since I wrote that manuscript with Jakob Stix.
“I think it is safe to say that there has not been much change in the community opinion since 2018,” says Kiran Kedlaya, a number theorist at the University of California, San Diego, who was among the experts who put considerable effort over several years trying to verify the proof.
I asked around this morning and no one I know who is well-informed about this has heard of any reason to change their opinion that Mochizuki does not have a proof.
Ivan Fesenko today has a long article entitled On Pioneering Mathematical Research, On the Occasion of Announcement of Forthcoming Publication of the IUT Papers by Shinichi Mochizuki. Much like earlier articles from him (I’d missed this one), it’s full of denunciations of anyone (including Scholze) who has expressed skepticism about the proof as an incompetent. There’s a lot about how Mochizuki’s work on the purported proof is an inspiration to the world, ending with:
In the UK, the recent new additional funding of mathematics, work on which was inspired by the pioneering research of Sh. Mochizuki, will address some of these issues.
which refers to the British government decision discussed here.
There is a really good inspirational story in recent years about successful pioneering mathematical research, but it’s the one about Scholze’s work, not the proof of abc that experts don’t believe, even if it gets published.
Update: See the comment posted here from Peter Scholze further explaining the underlying problem with the Mochizuki proof.